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13x=9x^2+2
We move all terms to the left:
13x-(9x^2+2)=0
We get rid of parentheses
-9x^2+13x-2=0
a = -9; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·(-9)·(-2)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{97}}{2*-9}=\frac{-13-\sqrt{97}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{97}}{2*-9}=\frac{-13+\sqrt{97}}{-18} $
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